Find the y - intercept of the line joining two points (1, 3) and (3,5)

Options

A. `-2`
B. 0
C. 2
D. 4

Answer

To find the y-intercept of the line joining the points (1, 3) and (3, 5), we can follow these steps:

### Step 1: Identify the points
We have two points:
- Point 1 (x1, y1) = (1, 3)
- Point 2 (x2, y2) = (3, 5)

### Step 2: Calculate the slope (m) of the line
The formula for the slope (m) of a line passing through two points is given by:
\[ m = \frac{y2 - y1}{x2 - x1} \]
Substituting the values:
\[ m = \frac{5 - 3}{3 - 1} = \frac{2}{2} = 1 \]

### Step 3: Use the point-slope form of the equation of the line
The point-slope form of the equation of a line is:
\[ y - y1 = m(x - x1) \]
Using point (1, 3):
\[ y - 3 = 1(x - 1) \]
This simplifies to:
\[ y - 3 = x - 1 \]
\[ y = x + 2 \]

### Step 4: Find the y-intercept
The y-intercept occurs when \(x = 0\). We substitute \(x = 0\) into the equation:
\[ y = 0 + 2 = 2 \]

### Final Answer
The y-intercept of the line joining the points (1, 3) and (3, 5) is \(2\).

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